Q72.If the point (1, 4) lies inside the circle x2 + y2 −6x + 10y + p = 0 and the circle does not touch or intersect the coordinate axes, then the set of all possible values of p is the interval (1) (25, 39) (2) (25, 29) (3) (0, 25) (4) (9, 25)
What This Question Tests
This question combines conditions for a point to lie inside a circle with conditions for a circle to not intersect or touch the coordinate axes, requiring solving inequalities.
Concepts Tested
Formulas Used
For x^2+y^2+2gx+2fy+c=0, point (x1,y1) is inside if x1^2+y1^2+2gx1+2fy1+c < 0
A circle does not touch or intersect x-axis if g^2-c < 0
A circle does not touch or intersect y-axis if f^2-c < 0
📚 NCERT Sections This Tests
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
Physics Class 12 · Chapter 9
9.17 (a) sin i¢c = 1.44/1.68 which gives i¢c = 59°. Total internal reflection takes place when i > 59° or when r < rmax = 31°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60°. Thus, all incident rays of angles in the range 0 < i < 60° will suffer total internal reflections in the pipe. (If the length of the pipe is finite, which it is in practice, there will be a lower limit on i determined by the ratio of the diameter to the length of the pipe.) (b) If there is no outer coating, i¢c = sin–1(1/1.68) = 36.5°. Now, i = 90° will have r = 36.5° and i¢ = 53.5° which is greater than i¢c. Thus, all incident rays (in the range 53.5° < i < 90°) will suffer total internal reflections.
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Circles
- Topic
- Position of a point relative to a circle
- Year
- 2014
- Shift
- 09 Apr Online
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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